Sökning: "envelope of holomorphy"

Hittade 4 avhandlingar innehållade orden envelope of holomorphy.

  1. 1. Envelopes of holomorphy for bounded holomorphic functions

    Författare :Ulf Backlund; Umeå universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; holomorphicfunction; boundedholomorphic function; domain of holo¬ morphy; envelope of holomorphy; Gleason’s problem; convex set; plurisubharmonic function; pluripolar set; poly normally convex set;

    Sammanfattning : Some problems concerning holomorphic continuation of the class of bounded holo­morphic functions from bounded domains in Cn that are domains of holomorphy are solved. A bounded domain of holomorphy Ω in C2 with nonschlicht H°°-envelope of holomorphy is constructed and it is shown that there is a point in D for which Glea­son’s Problem for H°°(Ω) cannot be solved. LÄS MER

  3. 2. Algebras of bounded holomorphic functions

    Författare :Anders Fällström; Umeå universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; holomorphic function; bounded holomorphic function; domain of holomorphy; envelope of holomorphy; Gleason’s problem; convex set; uniform algebra; spectrum; fibers; generalized Shilov boundary; analytic structure; plurisubharmonic function;

    Sammanfattning : Some problems concerning the algebra of bounded holomorphic functions from bounded domains in Cn are solved. A bounded domain of holomorphy Q in C2 with nonschlicht i7°°- envelope of holomorphy is constructed and it is shown that there is a point in Q for which Gleason’s Problem for H°°(Q) cannot be solved. LÄS MER

  4. 3. Polynomial Hulls and Envelopes of Holomorphy

    Författare :Lennart S. Nobel; Burglind Jöricke; Nikolay Shcherbina; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Cantor sets; polynomial hulls; envelopes of holomorphy; continuity principle; MATHEMATICS; MATEMATIK; matematik; Mathematics;

    Sammanfattning : The notion of polynomial hulls of compact subsets of complex Euclidean space plays a crucial role for approximation of holomorphic functions by polynomials - a topic which has many applications. Despite an abstract characterization of polynomial hulls in terms of currents, given by Duval and Sibony, it is often very difficult even for special classes of sets to decide whether the polynomial hull is trivial (i. LÄS MER

  5. 4. On Propagation of Boundary Continuity for Domains in Complex Space

    Författare :Salla Franzén; Egmont Porten; Jan-Erik Björk; Ragnar Sigurdsson; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Boundary behavior of holomorphic functions; Global boundary behavior of holomorphic functions; MATHEMATICS; MATEMATIK; matematik; Mathematics;

    Sammanfattning : We consider continuity properties of analytic functions in bounded domains in complex space, focusing on the following two questions:Question 1. Given a bounded domain G in complex affine n-space. LÄS MER